$\dfrac{ -10x + 3y }{ -8 } = \dfrac{ -5x + 6z }{ 3 }$ Solve for $x$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -10x + 3y }{ -{8} } = \dfrac{ -5x + 6z }{ 3 }$ $-{8} \cdot \dfrac{ -10x + 3y }{ -{8} } = -{8} \cdot \dfrac{ -5x + 6z }{ 3 }$ $-10x + 3y = -{8} \cdot \dfrac { -5x + 6z }{ 3 }$ Multiply both sides by the right denominator. $-10x + 3y = -8 \cdot \dfrac{ -5x + 6z }{ {3} }$ ${3} \cdot \left( -10x + 3y \right) = {3} \cdot -8 \cdot \dfrac{ -5x + 6z }{ {3} }$ ${3} \cdot \left( -10x + 3y \right) = -8 \cdot \left( -5x + 6z \right)$ Distribute both sides ${3} \cdot \left( -10x + 3y \right) = -{8} \cdot \left( -5x + 6z \right)$ $-{30}x + {9}y = {40}x - {48}z$ Combine $x$ terms on the left. $-{30x} + 9y = {40x} - 48z$ $-{70x} + 9y = -48z$ Move the $y$ term to the right. $-70x + {9y} = -48z$ $-70x = -48z - {9y}$ Isolate $x$ by dividing both sides by its coefficient. $-{70}x = -48z - 9y$ $x = \dfrac{ -48z - 9y }{ -{70} }$ Swap signs so the denominator isn't negative. $x = \dfrac{ {48}z + {9}y }{ {70} }$